strong adjoint functor
For a cartesian closed category and two endofunctors, they are called strong adjoints to each other if there is a natural isomorphism
[L X, A] \simeq [X, R A]
for all objects and for the internal hom.
Notice that for the terminal object of we have that the global points of the internal hom give the external hom set
\Gamma [X,A] := C(*, [X, A]) \simeq C(X,A)
Therefore strongly adjoint functors are in particular adjoint functors in the ordinary sense.
For instance appendix 6 of
Created on December 7, 2011 19:45:19
by Urs Schreiber